The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  1  1  1  1  1  X  1  1 X^2  1  1  1  X  1  X  1  0  1  1  1  X  1  X  1  1  X  1  1  0  1  1  1  1
 0  X  0  0  0  0  0 X^2 X^2  X X^2+X  X  X  X X^2+X  X  0 X^2+X X^2  X X^2  X  0  X X^2 X^2+X X^2+X X^2 X^2+X X^2 X^2+X  X  0  X X^2  X  X  0 X^2 X^2  0 X^2+X X^2+X  X  0  0  0  X  0 X^2  0 X^2  X X^2  X X^2+X  X X^2+X X^2+X X^2+X X^2+X
 0  0  X  0  0 X^2 X^2+X  X  X  X  X  X X^2+X  0  0  0 X^2 X^2 X^2+X  X X^2  0  0 X^2+X X^2 X^2  0  0  0 X^2+X X^2+X  X X^2+X  0  X X^2 X^2+X X^2  X  X X^2+X X^2+X  X  X  X  X X^2  X  0 X^2 X^2  0  0  0 X^2 X^2+X  X  0 X^2+X  0  X
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2+X X^2+X  0  0  X  X X^2  X X^2 X^2+X  0 X^2+X  0 X^2  X X^2  X  0  X  X  X  0  X X^2  X X^2 X^2+X X^2  0 X^2+X  X  X  0 X^2  X X^2 X^2  0 X^2+X X^2 X^2  X  0 X^2+X X^2  0  X  0  0  X X^2+X  X
 0  0  0  0  X  X X^2 X^2+X  X X^2+X X^2 X^2  X X^2 X^2+X  X  X X^2 X^2 X^2+X  0 X^2+X  0 X^2+X X^2+X X^2+X X^2  X  0  X  0 X^2  X X^2 X^2  0  0 X^2  0 X^2 X^2+X X^2+X  X X^2+X  0 X^2+X  0  0 X^2+X X^2  X  0  X X^2+X  0  X  0 X^2+X  0  0  0

generates a code of length 61 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+80x^54+4x^55+185x^56+68x^57+272x^58+88x^59+311x^60+188x^61+262x^62+116x^63+170x^64+28x^65+102x^66+16x^67+66x^68+4x^69+42x^70+32x^72+10x^74+2x^76+1x^100

The gray image is a linear code over GF(2) with n=244, k=11 and d=108.
This code was found by Heurico 1.16 in 0.359 seconds.